Quadratic Equations & Functions
Master factoring, the quadratic formula, and parabola properties.
Practice Problems
Solve: x² + 5x + 6 = 0
Identify a=1, b=5, c=6
Calculate discriminant
Apply formula
Find both solutions
x² + 5x + 6 = 0
f(x) = 2(x - 3)² + 1
Common Mistakes
Pro Tips & Shortcuts
SAT Tip: Know when to use formula vs. factoring. SAT often makes factoring easier.
SAT Tip: The coefficient a determines the direction and width of the parabola.
SAT Tip: If b² - 4ac > 0: two solutions. If = 0: one solution. If < 0: no real solutions.
SAT Tip: Try factoring first - it's usually faster than the quadratic formula when it works.
SAT Tip: Always check if a quadratic can be factored before using the formula.
SAT Tip: Be careful with signs! f(x) = (x - 3)² has vertex at x = +3, not -3.
Try factoring first - it's often faster when it works.
If a is negative, the parabola opens down (maximum point). If positive, it opens up (minimum point).
Remember: "negative b, plus or minus, square root, b squared minus 4ac, all over 2a"
If the equation is simple (like x² - 9 = 0), factoring is much quicker than the formula.
For x² + bx + c, list factor pairs of c and find which pair adds to b.
The vertex is the minimum point (if a > 0) or maximum point (if a < 0).
Desmos can graph the parabola to find x-intercepts (solutions).